ΔABC में AB = 8 सेमी है। BC पर स्थित एक बिन्दु D, कोण A को इस प्रकार समद्विभाजित करता है कि BD = 6 सेमी तथा DC = 7.5 सेमी है, तो CA की लंबाई ज्ञात कीजिये।

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RRB ALP Previous Paper 5 (Held On: 10 Aug 2018 Shift 3)
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  1. 12 सेमी
  2. 12.5 सेमी
  3. 10.5 सेमी
  4. 10 सेमी

Answer (Detailed Solution Below)

Option 4 : 10 सेमी
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दिया है:

ΔABC में, AB = 8 सेमी

BC को बिन्दु D पर समद्विभाजित करने के लिए ∠A को आंतरिक रूप से समद्विभाजित किया जाता है

AB = 8 सेमी, BD = 6 सेमी और DC = 7.5 सेमी

प्रयुक्त अवधारणा:

F1 SSC Priya 14-3-24 D22

एक त्रिभुज में, एक कोण का कोण समद्विभाजक कोण के विपरीत भुजा को शेष दो भुजाओं के अनुपात में विभाजित करता है।

\(\frac{AB}{AC} = \frac{BD}{DC}\)

गणना:

AB = 8 सेमी है और BC को बिन्दु D पर समद्विभाजित करने के लिए ∠A को आंतरिक रूप से समद्विभाजित किया जाता है,

⇒ AB/AC = BD/CD

⇒ 8/AC = 6/7.5

∴ AC = 10 सेमी

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